RED DOWN: Zach Parise, who got tied up with the Kings’ Jonathan Quick during the Stanley Cup Finals, could receive an offer from the Rangers as soon as today if the Devils captain shows serious interest in moving across the Hudson River. Photo: UPI

The dynamic will be unique.

For while Zach Parise will entertain presentations from an assortment of marquee teams pitching themselves and untold millions of dollars to the 27-year-old left wing — who will be the most sought after NHL free agent on the market if he is not signed by the Devils before noon today — it will be up to the Devils captain to pitch himself to the Rangers and convince management he truly does want to play in New York.

It’s an unlikely scenario, given Parise will no doubt be recruited by big-time franchises such as the Penguins, Flyers and Red Wings, all of whom have cap space to spare; and by the Wild, who have sent signals the organization intends to blow him out of the water with a contract offer in order to bring him home to the Twin Cities.

But the Rangers will surely listen if Parise indicates an interest in crossing the Hudson to sign up with the Devils’ mortal enemy. You bet they will.

The Blueshirts, who are in desperate search of a first-line left wing and whose general manager, Glen Sather, pledged last yesterday “to be as aggressive as possible in the free-agent market,” will surely allow Parise to recant the “No way” testimony he gave in the Devils’ dressing room two days after losing the Stanley Cup Finals to the Kings when asked if he would consider signing with the Rangers.

The question, though, is whether he truly does want to play in New York, whether this seven-season career Devil who recorded 69 points (31-38) last year could find a comfort level wearing the Blueshirt and thus become the first big-name player to successfully cross the divide.

If the call is made and the message is credible, the Rangers would act. Given the alternative of trading for Rick Nash or Bobby Ryan, the Rangers would not hesitate to dive in with a front-loaded, lockout-protected offer if they’re satisfied the offer would not be construed as a bribe.

Still, though, this is not a likely scenario.

It’s difficult to determine just who Sather might target over the next 48 hours. There is no credible right defenseman on the market to fill the second-pair hole on defense that remains wide open after University of Wisconsin free agent Justin Schultz’s decision yesterday to sign with the Oilers.

Rather than throw Monopoly money at marginal players — e.g., Jason Garrison — the Rangers might revisit a deal for the Coyotes’ Keith Yandle if the price becomes right as the summer evolves.

Ryan Suter, who will be the object of much affection, plays the wrong side; The Rangers believe they’re strong on the left lining up with Ryan McDonagh, Marc Staal and Michael Del Zotto.

Brandon Prust is all but gone, the valuable support player apparently in line for a contract under which he might earn at least $2.5 million per for three or four years.

Prust may give the Blueshirts a right to match, but it’s extremely unlikely the Rangers would commit that kind of money to a winger who gets less than 12 minutes of ice a game, no matter his intangibles.

Instead, the Blueshirts are likely to at least investigate the possibility of signing Jordin Tootoo, the 29-year-old, eight-season Predators veteran with the checkered history who could play a role similar to Prust.

Sather is likely to check in on Shane Doan, but it is believed the long-time Phoenix captain would prefer to remain out west even if he does not re-up with the Coyotes. The GM probably will check with Alex Semin of the Capitals, Jiri Hudler of the Red Wings, Brad Boyes of the Sabres and Ray Whitney of the Coyotes, but is unlikely to offer lucrative multi-year deals to entice any of them.